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Mole & Molar Mass

Mole concept: Avogadro constant, molar mass, and quick mass↔moles↔particles calculations with correct units and exam-ready steps.

  • SEC G3 Pure Chemistry 2027
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Learning objectives

  • define the term mole in terms of the Avogadro constant

Mole questions depend on clear quantities and units. Keep Mᵣ, molar mass, and number of specified entities distinct from the start.

1. Definition

One mole (mol) is the amount of substance that contains the Avogadro constant number of specified entities: 6.02 × 10²³ atoms, molecules, ions, or formula units.

The Avogadro constant (N_A) is:

N_A = 6.02 × 10²³ mol⁻¹

2. Key Ideas

  • Amount of substance is written as n and measured in moles (mol).
  • Molar mass M has units g mol⁻¹.
  • For a substance: M is numerically equal to Aᵣ or Mᵣ, but with units (g mol⁻¹).
  • Converting between mass, moles, and particles uses these two core equations:
    • n = m/M
    • N = nN_A

3. Detailed Explanations

Quick Recall (what you must know)
  • n = m/M where M is molar mass (g mol⁻¹).
  • N = nN_A where N_A = 6.02 × 10²³ mol⁻¹.
  • Mᵣ has no units; molar mass M has units.
  • “Particles” can mean atoms, molecules, ions, or formula units (check the question wording).

A. The Mole is a Counting Unit

Just like “a dozen” means 12 items, “a mole” means 6.02 × 10²³ particles.

The particle can be atoms, molecules, ions, or formula units (for ionic compounds).

B. Molar Mass (M)

Molar mass M is the mass of 1 mole of a substance.

  • For elements: M is based on Aᵣ (from the periodic table).
  • For compounds: M is based on Mᵣ / relative formula mass.
Mᵣ vs M

Mᵣ has no units.
Molar mass M has units g mol⁻¹.

C. Two Core Equations (Write Them Every Time)

n = m/M; N = nN_A

Where:

  • n = moles (mol)
  • m = mass (g)
  • M = molar mass (g mol⁻¹)
  • N = number of particles (count)
  • N_A = 6.02 × 10²³ mol⁻¹
Mass, moles and entities conversion mapMass in grams converts to moles by dividing by molar mass, and moles convert back to mass by multiplying by molar mass. Moles convert to entities by multiplying by the Avogadro constant, and entities convert to moles by dividing by it.Mass, mgrams (g)measured or calculatedAmount, nmoles (mol)the stoichiometric bridgeEntities, Na count (no unit)state atom, molecule, ionor formula unit÷ M× M× NA÷ NAn = m/M · N = nNANA = 6.02 × 10²³ mol⁻¹ · M is molar mass in g mol⁻¹
Use moles as the bridge between mass and number of specified entities. Relative mass has no units; molar mass M is measured in g mol⁻¹.

4. Common Mistakes

  • Writing N_A = 6.02 × 10²³ without units (write mol⁻¹).
  • Using Mᵣ as if it has units of g mol⁻¹ without stating it is molar mass M.
  • Forgetting that “particles” could mean atoms, molecules, ions, or formula units.
  • Counting atoms wrongly: 1 molecule of CO₂ has 3 atoms; 1 molecule of H₂O has 3 atoms.
  • Not using consistent units (mass in g, not mg; if mg is given, convert).

5. Exam Tips

Method that scores
  1. Find M (g mol⁻¹) 2) Find n using n = m/M 3) Convert to particles if needed using N = nN_A.
Particles trap

If the question asks for “number of atoms” in a molecular substance, multiply by atoms per molecule at the end.

6. Worked Examples

Modelled example 1

Mass → Moles (Water)

Core

Problem

Calculate the number of moles in 9.0 g of water, H₂O. Given Aᵣ(H) = 1, Aᵣ(O) = 16.
Study the worked solution

  1. Calculate molar mass

    Method

    Add the relative masses for two H atoms and one O atom.

    Reason

    The formula H₂O determines the mass of one mole of water molecules.

    Working

    M(H₂O) = 2(1) + 16 = 18 g mol⁻¹.

  2. Convert mass to amount

    Method

    Divide the sample mass by molar mass.

    Reason

    n = m/M converts grams into moles.

    Working

    n = 9.0/18 = 0.50 mol.

  3. Check the scale

    Method

    Compare 9.0 g with the mass of one mole.

    Reason

    9.0 g is half of 18 g, so the amount should be half a mole.

    Working

    n(H₂O) = 0.50 mol.

Guided practice 2

Moles → Particles (Molecules)

About 5 min

Problem

How many molecules are present in 0.25 mol of carbon dioxide, CO₂?

Use the Avogadro constant

Hints

Hint 1: choose the direction
Starting with moles and finding particles means multiply by N_A.
Hint 2: substitute
N = 0.25 × 6.02 × 10²³.
View solution step by step

  1. Choose the particle equation

    Method

    Use N = nN_A.

    Reason

    One mole contains 6.02 × 10²³ specified entities.

    Working

    N = 0.25 × 6.02 × 10²³.

  2. Calculate and name the entity

    Method

    Multiply and attach the requested particle label.

    Reason

    The question asks for molecules, not atoms.

    Working

    N = 1.505 × 10²³ molecules.

Common misconception 3

“Atoms” Trap (CO2)

Find and correct the mistake

Learner response

How many atoms are there in 0.10 mol of CO₂ molecules? A student gives 6.02 × 10²² atoms because they multiply only by N_A. Explain the mistake and correct the answer.

Separate molecule count from atom count

Missing step

View solution step by step

  1. Find molecules first

    Method

    Convert 0.10 mol into the number of CO₂ molecules.

    Reason

    N_A counts the specified entities, which here are molecules.

    Working

    N(molecules) = 0.10 × 6.02 × 10²³ = 6.02 × 10²².

  2. Count atoms in each molecule

    Method

    Read one C and two O atoms from CO₂.

    Reason

    Each molecule therefore contains three atoms altogether.

    Working

    1 + 2 = 3 atoms per molecule.

  3. Correct the result

    Method

    Multiply the molecule count by three.

    Reason

    The required entity is atoms, not molecules.

    Working

    N(atoms) = 3(6.02 × 10²²) = 1.806 × 10²³ atoms.

Examiner practice 4

Mass → Particles (Atoms)

4 marks

Examination question

Calculate the number of atoms in 4.0 g of magnesium. Given Aᵣ(Mg) = 24. [4 marks]

Show the molar-mass and mole steps

View solution step by step

  1. State molar mass

    1 mark

    Method

    Convert the supplied Aᵣ into molar mass.

    Reason

    Mass-to-mole calculations require M in g mol⁻¹.

    Working

    M(Mg) = 24 g mol⁻¹.

  2. Find moles

    1 mark

    Method

    Divide mass by molar mass.

    Reason

    n = m/M.

    Working

    n = 4.0/24 = 0.1667 mol.

  3. Convert to atoms

    1 mark

    Method

    Multiply moles by N_A.

    Reason

    Magnesium is monatomic, so the specified entities are atoms.

    Working

    N = 0.1667 × 6.02 × 10²³.

  4. Report the answer

    1 mark

    Working

    N ≈ 1.00 × 10²³ atoms.

Challenge 5

Particles → Moles

Minimal support

Reverse-direction transfer

How many moles are in 3.01 × 10²³ molecules of CO₂?

Reverse the Avogadro conversion

Hints

Hint 1: reverse direction
Particles to moles uses division by N_A, the reverse of N = nN_A.
View solution step by step

  1. Rearrange the relationship

    Method

    Use n = N/N_A.

    Reason

    The number of particles is known and the amount is unknown.

    Working

    n = (3.01 × 10²³)/(6.02 × 10²³).

  2. Cancel the common power and calculate

    Method

    Divide the coefficients.

    Reason

    The common factor 10²³ cancels.

    Working

    n = 3.01/6.02 = 0.50 mol.

7. Mind Stretchers

Mind stretcher 1: Ions From a Formula UnitExtension

Question: 0.20 mol of sodium chloride dissolves completely. How many chloride ions, Cl⁻, are formed?

Show Answer

Each formula unit of NaCl gives 1 Cl⁻ ion.

So moles of Cl⁻ formed = 0.20 mol.

N(Cl⁻) = 0.20 × 6.02 × 10²³; = 1.204 × 10²³ ions

Mind stretcher 2: Error Analysis (Wrong Units)Extension

Question: A student writes: “Mᵣ(H₂O) = 18 g mol⁻¹”. What is wrong, and what should it be?

Show Answer

Mᵣ has no units. Mᵣ(H₂O) = 18.

The molar mass is M(H₂O) = 18 g mol⁻¹.

8. Quiz

Quiz time

Ready to check your understanding? Try the interactive quiz, then review any questions you missed.

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